Legendrian framings for two-bridge links

Abstract

We define the Thurston-Bennequin polytope of a two-component link as the convex hull of all pairs of integers that arise as framings of a Legendrian representative. The main result of this paper is a description of the Thurston-Bennequin polytope for two-bridge links. As an application, we construct non-quasipositive surfaces in R 3 \mathbb {R}^3 all of whose sub-annuli are quasipositive.